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Proof step 3 from proof reachable-n-rec-rev (previous step)

⊦ reachable-n(H, n + 1, r, r0) ∧ n < n + 1, reachable-n(H, n + 1, r, r0) ↔ (∃ r1. reachable-n(H, n, r, r1) ∧ reachable-1(H, r1, r0))

User applied rule case distinction

And obtained the following new goals

Proof step 4:
reachable-n(H, n + 1, r, r0) ⊦ ∃ r1. reachable-n(H, n, r, r1) ∧ reachable-1(H, r1, r0), reachable-n(H, n + 1, r, r0) ∧ n < n + 1
Proof step 5:
∃ r1. reachable-n(H, n, r, r1) ∧ reachable-1(H, r1, r0) ⊦ reachable-n(H, n + 1, r, r0), reachable-n(H, n + 1, r, r0) ∧ n < n + 1

Rule argument

pos: right 2

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